Plots for example with Insulated Ends
> | with(plots): |
Fourier series of the even periodic extension of sin(x) on [0,Pi].
> | plot(2/Pi + 4/Pi * sum(cos(2*k*x)*exp(-4*k^2*0)/(1-4*k^2),k=1..30),x=-3*Pi..3*Pi,color=plum,thickness=2,numpoints=1000,title="Even Extension"); |
Integral for coefficients.
> | int(sin(x)*cos(n*x),x=0..Pi); |
Plots for various times.
> | plot([2/Pi + 4/Pi * sum(cos(2*k*x)*exp(-4*k^2*0)/(1-4*k^2),k=1..30),2/Pi],x=-0..Pi,thickness=2,view=0..1.3,title="t=0.0"); |
> | plot([2/Pi + 4/Pi * sum(cos(2*k*x)*exp(-4*k^2*0.01)/(1-4*k^2),k=1..30),2/Pi],x=-0..Pi,thickness=2,view=0..1.3,title="t=0.01"); |
> | plot([2/Pi + 4/Pi * sum(cos(2*k*x)*exp(-4*k^2*0.02)/(1-4*k^2),k=1..30),2/Pi],x=-0..Pi,thickness=2,view=0..1.3,title="t=0.02"); |
> | plot([2/Pi + 4/Pi * sum(cos(2*k*x)*exp(-4*k^2*0.03)/(1-4*k^2),k=1..30),2/Pi],
x=0..Pi,thickness=2,view=0..1.3,title="t=0.03"); |
> | plot([2/Pi + 4/Pi * sum(cos(2*k*x)*exp(-4*k^2*0.05)/(1-4*k^2),k=1..30),2/Pi],
x=0..Pi,thickness=2,view=0..1.3,title="t=0.05"); |
> | plot([2/Pi + 4/Pi * sum(cos(2*k*x)*exp(-4*k^2*0.1)/(1-4*k^2),k=1..30),2/Pi],
x=0..Pi,thickness=2,view=0..1.3,title="t=0.1"); |
> | plot([2/Pi + 4/Pi * sum(cos(2*k*x)*exp(-4*k^2*0.2)/(1-4*k^2),k=1..30),2/Pi],
x=0..Pi,thickness=2,view=0..1.3,title="t=0.2"); |
> | plot([2/Pi + 4/Pi * sum(cos(2*k*x)*exp(-4*k^2*0.3)/(1-4*k^2),k=1..30),2/Pi],
x=0..Pi,thickness=2,view=0..1.3,title="t=0.3"); |
> | plot([2/Pi + 4/Pi * sum(cos(2*k*x)*exp(-4*k^2*0.6)/(1-4*k^2),k=1..30),2/Pi],
x=0..Pi,thickness=2,view=0..1.3,title="t=0.6"); |
> | plot([2/Pi + 4/Pi * sum(cos(2*k*x)*exp(-4*k^2*1.0)/(1-4*k^2),k=1..30),2/Pi],
x=0..Pi,thickness=2,view=0..1.3,title="t=1.0"); |
> |
> |
The animation.
> | a:=animate(2/Pi + 4/Pi * sum(cos(2*k*x)*exp(-4*k^2*t)/(1-4*k^2),k=1..30),
x=0..Pi,t=0..1,thickness=2,view=0..1.3,title="Animation for Insultated Ends Example"): |
> | ave:=plot(2/Pi,x=0..Pi,color=green,thickness=2,view=0..1.3): |
> | display(a,ave); |
> |